{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# KLD\n",
    "\n",
    "相对熵（relative entropy）又称为KL散度（Kullback–Leibler divergence，简称KLD），信息散度（information divergence），信息增益（information gain）。\n",
    "\n",
    "KL散度是两个概率分布P和Q差别的非对称性的度量。\n",
    "\n",
    "根据shannon的信息论，给定一个字符集的概率分布，我们可以设计一种编码，使得表示该字符集组成的字符串平均需要的比特数最少。假设这个字符集是X，对$x \\in X$，其出现概率为$P(x)$，那么其最优编码平均需要的比特数等于这个字符集的熵：\n",
    "\n",
    "$$\n",
    "H(X) = \\sum_{x \\in X} P(x)log[1/P(x)] = - \\sum_{x \\in X} P(x)log[P(x)]\n",
    "$$\n",
    "\n",
    "一个系统越是有序，那么它的信息熵就越低，反之就越高。\n",
    "\n",
    "两个分布的距离:\n",
    "$$\n",
    "D_{KL}(Q||P) = \\sum_{x \\in X} Q(x)[log(1/P(x))] - \\sum_{x \\in X} Q(x)[log[1/Q(x)]] = \\sum_{x \\in X} Q(x)log[Q(x)/P(x)]\n",
    "$$\n",
    "\n",
    "又叫交叉熵:\n",
    "$$\n",
    "D_{KL} (P || Q) =-H(P) + -H(P, Q)\n",
    "$$\n",
    "\n",
    "KL-divergence始终是大于等于0的。当且仅当两分布相同时，KL-divergence等于0.(The KL divergence is 0 only when P and Q have the same distribution.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## JSD\n",
    "\n",
    "The gabove KL divergence is asymmetric, which is inconvenient. Therefore, Jensen-Shannon (JS) divergence is an index defined to be symmetric.\n",
    "\n",
    "$$\n",
    "D_{JS} =\\frac{1}{2}D_{KL}(P||M)+\\frac{1}{2}D_{KL}(Q||M) \\\\ (where\\  M(x) = \\frac{P(x)+Q(X)}{2})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import norm, entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10.0, 10.0, 10000)\n",
    "\n",
    "#Figure size\n",
    "plt.figure(figsize = (16, 8))\n",
    "\n",
    "# 3x3 subplot\n",
    "for i in np.arange(3):\n",
    "    for j in np.arange(3):\n",
    "        index = i * 3 + j\n",
    "   \n",
    "        # Define each probability distribution\n",
    "        p = norm.pdf(x, loc = 0, scale = 1)\n",
    "        q = norm.pdf(x, loc = index * 0.5, scale = 1)\n",
    "        # probability distribution of the mean of p and q\n",
    "        m = (p + q) / 2\n",
    "   \n",
    "        # Calculation of KL divergence and JS divergence\n",
    "        kl = entropy(p, q)\n",
    "        kl_pm = entropy(p, m)\n",
    "        kl_qm = entropy(q, m)\n",
    "        js = (kl_pm + kl_qm) / 2\n",
    "   \n",
    "        # subplot\n",
    "        plt.subplot (3, 3, i * 3 + j + 1)\n",
    "        # Shape fill\n",
    "        plt.fill_between (x, m, facecolor = \"y\", alpha = 0.2, label='m')\n",
    "        plt.fill_between (x, p, facecolor = \"b\", alpha = 0.2, label='p')\n",
    "        plt.fill_between (x, q, facecolor = \"r\", alpha = 0.2, label='q')\n",
    "        # Below formatting\n",
    "        plt.xlim (-5, 7)\n",
    "        plt.ylim (0, 0.45)\n",
    "        plt.title (\"KLD: {:>.3f}\".format(kl) + \", JSD: {:>.3f}\".format(js))\n",
    "        plt.legend()\n",
    "        # plt.tick_params(labelbottom = False)\n",
    "        # plt.tick_params(labelleft = False)\n",
    "  \n",
    "plt.subplots_adjust (wspace = 0.1, hspace = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "[浅谈KL散度](https://www.cnblogs.com/hxsyl/p/4910218.html)\n",
    "\n",
    "[KLD,JSD可視化](http://yusuke-ujitoko.hatenablog.com/entry/2017/05/07/200022)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
